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How the World Computes

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Cover of 'How the World Computes'

Table of Contents

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    Book Overview
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    Chapter 1 Ordinal Analysis and the Infinite Ramsey Theorem
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    Chapter 2 Curiouser and Curiouser: The Link between Incompressibility and Complexity
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    Chapter 3 Information and Logical Discrimination
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    Chapter 4 Robustness of Logical Depth
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    Chapter 5 Turing’s Normal Numbers: Towards Randomness
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    Chapter 6 Logic of Ruler and Compass Constructions
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    Chapter 7 How the World Computes
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    Chapter 8 Square Roots and Powers in Constructive Banach Algebra Theory
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    Chapter 9 How the World Computes
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    Chapter 10 A Note on Ramsey Theorems and Turing Jumps
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    Chapter 11 Automatic Functions, Linear Time and Learning
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    Chapter 12 An Undecidable Nested Recurrence Relation
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    Chapter 13 How the World Computes
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    Chapter 14 On Mathias Generic Sets
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    Chapter 15 Complexity of Deep Inference via Atomic Flows
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    Chapter 16 Connecting Partial Words and Regular Languages
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    Chapter 17 Randomness, Computation and Mathematics
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    Chapter 18 Learning, Social Intelligence and the Turing Test - why an "out-of-the-box" Turing Machine will not pass the Turing Test
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    Chapter 19 Confluence in Data Reduction: Bridging Graph Transformation and Kernelization
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    Chapter 20 Highness and Local Noncappability
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    Chapter 21 Turing Progressions and Their Well-Orders
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    Chapter 22 A Short Note on Spector’s Proof of Consistency of Analysis
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    Chapter 23 Sets of Signals, Information Flow, and Folktales
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    Chapter 24 On the Foundations and Philosophy of Info-metrics
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    Chapter 25 On Mathematicians Who Liked Logic
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    Chapter 26 Densities and Entropies in Cellular Automata
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    Chapter 27 Foundational Analyses of Computation
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    Chapter 28 Turing Machine-Inspired Computer Science Results
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    Chapter 29 NP-Hardness and Fixed-Parameter Tractability of Realizing Degree Sequences with Directed Acyclic Graphs
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    Chapter 30 A Direct Proof of Wiener’s Theorem
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    Chapter 31 Effective Strong Nullness and Effectively Closed Sets
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    Chapter 32 Word Automaticity of Tree Automatic Scattered Linear Orderings Is Decidable
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    Chapter 33 On the Relative Succinctness of Two Extensions by Definitions of Multimodal Logic
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    Chapter 34 On Immortal Configurations in Turing Machines
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    Chapter 35 A Slime Mold Solver for Linear Programming Problems
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    Chapter 36 Multi-scale Modeling of Gene Regulation of Morphogenesis
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    Chapter 37 Tree-Automatic Well-Founded Trees
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    Chapter 38 Infinite Games and Transfinite Recursion of Multiple Inductive Definitions
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    Chapter 39 A Hierarchy of Immunity and Density for Sets of Reals
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    Chapter 40 How Much Randomness Is Needed for Statistics?
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    Chapter 41 Towards a Theory of Infinite Time Blum-Shub-Smale Machines
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    Chapter 42 Turing Pattern Formation without Diffusion
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    Chapter 43 Degrees of Total Algorithms versus Degrees of Honest Functions
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    Chapter 44 A 5n − o(n) Lower Bound on the Circuit Size over U 2 of a Linear Boolean Function
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    Chapter 45 Local Induction and Provably Total Computable Functions: A Case Study
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    Chapter 46 What is Turing’s Comparison between Mechanism and Writing Worth?
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    Chapter 47 Substitutions and Strongly Deterministic Tilesets
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    Chapter 48 The Computing Spacetime
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    Chapter 49 Unifiability and Admissibility in Finite Algebras
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    Chapter 50 Natural Signs
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    Chapter 51 Characteristics of Minimal Effective Programming Systems
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    Chapter 52 After Turing: Mathematical Modelling in the Biomedical and Social Sciences
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    Chapter 53 Existence of Faster Than Light Signals Implies Hypercomputation Already in Special Relativity
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    Chapter 54 Turing Computable Embeddings and Coding Families of Sets
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    Chapter 55 On the Behavior of Tile Assembly System at High Temperatures
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    Chapter 56 Abstract Partial Cylindrical Algebraic Decomposition I: The Lifting Phase
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    Chapter 57 How the World Computes
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    Chapter 58 Relative Randomness for Martin-Löf Random Sets
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    Chapter 59 On the Tarski-Lindenbaum Algebra of the Class of all Strongly Constructivizable Prime Models
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    Chapter 60 Lower Bound on Weights of Large Degree Threshold Functions
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    Chapter 61 What Are Computers (If They’re not Thinking Things)?
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    Chapter 62 Compactness and the Effectivity of Uniformization
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    Chapter 63 On the Computability Power of Membrane Systems with Controlled Mobility
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    Chapter 64 On Shift Spaces with Algebraic Structure
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    Chapter 65 Finite State Verifiers with Constant Randomness
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    Chapter 66 Game Arguments in Computability Theory and Algorithmic Information Theory
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    Chapter 67 Turing Patterns in Deserts
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    Chapter 68 Subsymbolic Computation Theory for the Human Intuitive Processor
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    Chapter 69 A Correspondence Principle for Exact Constructive Dimension
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    Chapter 70 Low n Boolean Subalgebras
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    Chapter 71 Bringing Up Turing’s ‘Child-Machine’
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    Chapter 72 Is Turing’s Thesis the Consequence of a More General Physical Principle?
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    Chapter 73 Some Natural Zero One Laws for Ordinals Below ε 0
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    Chapter 74 On the Road to Thinking Machines: Insights and Ideas
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    Chapter 75 Making Solomonoff Induction Effective
Attention for Chapter 17: Randomness, Computation and Mathematics
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Chapter title
Randomness, Computation and Mathematics
Chapter number 17
Book title
How the World Computes
Published in
Lecture notes in computer science, June 2012
DOI 10.1007/978-3-642-30870-3_17
Book ISBNs
978-3-64-230869-7, 978-3-64-230870-3
Authors

Rod Downey, Downey, Rod

Editors

S. Barry Cooper, Anuj Dawar, Benedikt Löwe

Mendeley readers

Mendeley readers

The data shown below were compiled from readership statistics for 3 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
Unknown 3 100%

Demographic breakdown

Readers by professional status Count As %
Professor > Associate Professor 1 33%
Unknown 2 67%
Readers by discipline Count As %
Computer Science 1 33%
Agricultural and Biological Sciences 1 33%
Unknown 1 33%